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Luden [163]
2 years ago
6

If x=6 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the equa

tion?
Mathematics
1 answer:
prisoha [69]2 years ago
8 0
If x=6 is the only intercept, it means that the quadratic is tangential to the x-axis, or equivalently x=6 is a root with multiplicity 2.
The discriminant is typically zero for multiplicity 2 in a quadratic. 
It will be clear looking at the quadratic formula:
if D=b^2-4ac = discriminant of the quadratic, then
x1=(-b+sqrt(D))/2a or x2=(-b-sqrt(D))/2a
if x1=x2 (double root, or multiplicity 2) then clearly D has to be zero.
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The admission fee at a movie theater is $5 for children and $9 for adults. If 3200 people go to the movies and $24000 is collect
Usimov [2.4K]
For this problem, let x be the number of children and y for adults. Formulate the equations: 1st equation, x + y = 3,200 and 2nd equation 5x + 9y = 24,000. Re-arrange 1st equation into x = 3200 - y. Then, substitute into 2nd equation, 5(3,200-y) + 9y = 24,000. Then, solve for y. The 16,000 - 5y + 9y = 24000. Final answer is, y = 2000 adults went to watch the movie.
6 0
2 years ago
a box holds nine smaller boxes. each of the smaller boxes holds nine plastic containers. each plastic contai.er holds nine bags.
svp [43]
So, basically ..you just multiply
9*9*9*9
6561
4 0
2 years ago
Given that a 90% confidence interval for the mean height of all adult males in Idaho measured in inches was [62.532, 76.478]. Us
grigory [225]

Answer:

The confidence interval on this case is given by:

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}} (1)

For this case the confidence interval is given by (62.532, 76.478)[/tex]

And we can calculate the mean with this:

\bar X = \frac{62.532+76.478}{2}= 69.505

So then the mean for this case is 69.505

Step-by-step explanation:

Previous concepts

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

\bar X represent the sample mean  

\mu population mean (variable of interest)  

\sigma represent the population standard deviation  

n represent the sample size  

Assuming the X follows a normal distribution  

X \sim N(\mu, \sigma)

The confidence interval on this case is given by:

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}} (1)

For this case the confidence interval is given by (62.532, 76.478)[/tex]

And we can calculate the mean with this:

\bar X = \frac{62.532+76.478}{2}= 69.505

So then the mean for this case is 69.505

5 0
2 years ago
Divide 794.1 by 7.61. Round off your answer to two decimal places. A. 104.35 B. 786.49 C. 95.83 D. 1,043.50
VikaD [51]
Answer: 
A. 104.35

Explanation: 
794.1 ÷ 7.61 = 104.34954 
Round off to two decimal places: 
104.349 
round 4 up to 5 because the next number is greater than 5: 
9 > 5 
So 
104.35
3 0
2 years ago
Read 2 more answers
On a piece of paper, graph y&lt; x-3. Then determine which answer matches<br> the graph you drew
Aneli [31]

Answer:

The graph is shown below.

Step-by-step explanation:

Given:

The inequality of a line to graph is given as:

y

In order to graph it, we first make the 'inequality' sign to 'equal to' sign. This gives,

y=x-3

Now, we plot this line on a graph. The given line is of the form:

y=mx+b Where, 'm' is the slope and 'b' is the y-intercept.

So, for the line y=x-3, m=1,b=-3

The y-intercept is at (0, -3).

In order to draw the line correctly we find another point. Let the 'y' value be 0.

Now, 0=x-3\\x=3

So, the point is (3, 0).

Now, we mark these points and draw a line passing through these two points.

Now, consider the line inequality y. The 'y' value is less than x-3. So, the solution region will be region below the line and excluding all the points on the line. So, we draw a broken line and shade the region below it.

The graph is shown below.

5 0
2 years ago
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